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 A004014 Norms of vectors in the b.c.c. lattice. (Formerly M2347) 4
 0, 3, 4, 8, 11, 12, 16, 19, 20, 24, 27, 32, 35, 36, 40, 43, 44, 48, 51, 52, 56, 59, 64, 67, 68, 72, 75, 76, 80, 83, 84, 88, 91, 96, 99, 100, 104, 107, 108, 115, 116, 120, 123, 128, 131, 132, 136, 139, 140, 144, 147, 148, 152, 155, 160, 163, 164, 168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Integers such that A004013(n) is nonzero. - Michael Somos, Jul 28 2014 A subsequence of A047458. The complement seems to be 4*A004215. - Andrey Zabolotskiy, Nov 11 2021 From Mohammed Yaseen, Nov 06 2022: (Start) These are numbers of the form x^2+y^2+z^2 where x, y and z are either all even (including zero) or all odd. The selection rule for the planes with Miller indices (hkl) to undergo X-ray diffraction in an f.c.c. lattice is h^2+k^2+l^2 = N where N is a term of this sequence. See A000378 for simple cubic lattice. (End) REFERENCES J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 116. (Chapter 4 section 6.7) N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Robert Israel, Table of n, a(n) for n = 0..10000 G. Nebe and N. J. A. Sloane, Home page for this lattice Index entries for sequences related to b.c.c. lattice MAPLE f:= JacobiTheta2(0, z^4)^3+JacobiTheta3(0, z^4)^3: S:= series(f, z, 1001): select(t -> coeff(S, z, t) <> 0, [\$0..1000]); # Robert Israel, Oct 18 2015 MATHEMATICA f = EllipticTheta[2, 0, z^4]^3 + EllipticTheta[3, 0, z^4]^3; S = f + O[z]^200; Flatten[Position[CoefficientList[S, z], _?Positive] - 1] (* Jean-François Alcover, Oct 23 2016, after Robert Israel *) CROSSREFS Cf. A004013, A047458, A004215. Union of A034045 and A017101. - Mohammed Yaseen, Nov 06 2022 Sequence in context: A222269 A310011 A047458 * A243177 A113294 A169691 Adjacent sequences: A004011 A004012 A004013 * A004015 A004016 A004017 KEYWORD nonn,nice,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, Oct 17 2015 STATUS approved

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Last modified April 16 20:04 EDT 2024. Contains 371754 sequences. (Running on oeis4.)